Problem: Simplify the following expression: $ y = \dfrac{-8}{5} + \dfrac{2}{n - 3} $
Answer: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{n - 3}{n - 3}$ $ \dfrac{-8}{5} \times \dfrac{n - 3}{n - 3} = \dfrac{-8n + 24}{5n - 15} $ Multiply the second expression by $\dfrac{5}{5}$ $ \dfrac{2}{n - 3} \times \dfrac{5}{5} = \dfrac{10}{5n - 15} $ Therefore $ y = \dfrac{-8n + 24}{5n - 15} + \dfrac{10}{5n - 15} $ Now the expressions have the same denominator we can simply add the numerators: $y = \dfrac{-8n + 24 + 10}{5n - 15} $ $y = \dfrac{-8n + 34}{5n - 15}$